Question

1. Chris claims that the average weight of tears shed by each student after an quiz is more than 30 grams. You ask 42 random students if you could collect their tears after an quiz and find that the average weight was 30.3 grams. Assume the population standard deviation is 1 gram. At α = 0.1 is there enough evidence to support Chris’ claim?

Answer 1

given data are:-

sample size (n) = 42

sample mean () = 30.3

T

population sd ($\sigma$) = 1

hypothesis:-

$H_{0}:\mu=30$

H: > 30

the test statistic be:-

T- Z = 30.3 – 30 1/42 1.9442 0/ n

the p value is :-

$=P(Z>1.9442)$

$=1-P(Z<1.9442)$

$=1-\Phi(1.9442)$

$=1-0.9741$ [ in any blank cell of excel type =NORMSDIST(1.9442) ]

$=\mathbf{0.0259}$

decision:-

p value = 0.0259 < 0.1 (alpha)

we reject the null hypothesis. There is enough evidence to support Chris claim.

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